Evaluating Density Forecasts with an Application to Stock Market Returns
Density forecasts have become quite important in economics and finance. For example, such forecasts play a central role in modern financial risk management techniques like Value at Risk. This paper suggests a regression based density forecast evaluation framework as a simple alternative to other approaches. In simulation experiments and an empirical application to in- and out-of-sample one-step-ahead density forecasts of daily returns on the S&P 500, DAX and ATX stock market indices, the regression based evaluation strategy is compared with a recently proposed methodology based on likelihood ratio tests. It is demonstrated that misspecifications of forecasting models can be detected within the proposed regression framework. It is further demonstrated that the likelihood ratio methodology without additional misspecification tests has no power in many practical situations and therefore frequently selects incorrect forecasting models. The empirical results provide some evidence that GARCH-t models provide good density forecasts. The results further suggest that extensions of statistical models with fat-tailed conditional distributions to models that incorporate higher order conditional moments beyond the conditional variance might be appropriate to capture the empirical regularities in financial time series in some cases.
|Date of creation:||18 Feb 2002|
|Date of revision:|
|Contact details of provider:|| Postal: P.O. Box 61, A-1011 Vienna, Austria|
Phone: +43/1/404 20 7205
Fax: +43/1/404 20 7299
Web page: http://www.oenb.at/
More information through EDIRC
|Order Information:|| Postal: Oesterreichische Nationalbank, Economic Studies Division, c/o Beate Hofbauer-Berlakovich, POB 61, A-1011 Vienna, Austria|
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Hansen, B.E., 1992.
"Autoregressive Conditional Density Estimation,"
RCER Working Papers
322, University of Rochester - Center for Economic Research (RCER).
- Francis X. Diebold & Todd A. Gunther & Anthony S. Tay, 1997.
"Evaluating Density Forecasts,"
Center for Financial Institutions Working Papers
97-37, Wharton School Center for Financial Institutions, University of Pennsylvania.
- Francis X. Diebold & Todd A. Gunther & Anthony S. Tay, 1997. "Evaluating density forecasts," Working Papers 97-6, Federal Reserve Bank of Philadelphia.
- Francis X. Diebold & Todd A. Gunther & Anthony S. Tay, 1997. "Evaluating Density Forecasts," NBER Technical Working Papers 0215, National Bureau of Economic Research, Inc.
- Francis X. Diebold & Todd A. Gunther & Anthony S. Tay, . "Evaluating Density Forecasts," CARESS Working Papres 97-18, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences.
- Bollerslev, Tim, 1986.
"Generalized autoregressive conditional heteroskedasticity,"
Journal of Econometrics,
Elsevier, vol. 31(3), pages 307-327, April.
- Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
- Francis X. Diebold & Anthony S. Tay & Kenneth F. Wallis, 1997.
"Evaluating Density Forecasts of Inflation: The Survey of Professional Forecasters,"
NBER Working Papers
6228, National Bureau of Economic Research, Inc.
- Francis X. Diebold & Anthony S. Tay & Kenneth F. Wallis, 1998. "Evaluating Density Forecasts of Inflation: The Survey of Professional Forecasters," Working Papers 98-15, New York University, Leonard N. Stern School of Business, Department of Economics.
- Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993.
" On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks,"
Journal of Finance,
American Finance Association, vol. 48(5), pages 1779-1801, December.
- Lawrence R. Glosten & Ravi Jagannathan & David E. Runkle, 1993. "On the relation between the expected value and the volatility of the nominal excess return on stocks," Staff Report 157, Federal Reserve Bank of Minneapolis.
- Lumsdaine, Robin L, 1996. "Consistency and Asymptotic Normality of the Quasi-maximum Likelihood Estimator in IGARCH(1,1) and Covariance Stationary GARCH(1,1) Models," Econometrica, Econometric Society, vol. 64(3), pages 575-96, May.
- Francis X. Diebold & Jinyong Hahn & Anthony S. Tay, 1999. "Multivariate Density Forecast Evaluation And Calibration In Financial Risk Management: High-Frequency Returns On Foreign Exchange," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 661-673, November.
- Clements, M.P. & Smith J., 1998. "Evaluating The Forecast of Densities of Linear and Non-Linear Models: Applications to Output Growth and Unemployment," The Warwick Economics Research Paper Series (TWERPS) 509, University of Warwick, Department of Economics.
When requesting a correction, please mention this item's handle: RePEc:onb:oenbwp:59. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Markus Knell and Helmut Stix)
If references are entirely missing, you can add them using this form.